C2 chapter 1 - algebra and functions

"In this chapter you will learn how to do algebraic division and how to use the Remainder and Factor Theorems."

Sections

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C2 section 1.1

You need to be able to: factorise simple quadratics and the rules for working with fractions

You will learn how to simplify algebraic fractions by factorisation and cancelling common factors

Examples:

C2 Exercise 1A

• C2 Exercise 1A worked solutions:

Questions similar to this exercise:

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C2 section 1.2

You need to already know and understand the long division algorithm for integer division:

You will learn how to divide a polynomial by a binomial term (x ± k) for integer constant values k
Examples:

C2 Exercise 1B

• C2 Exercise 1B worked solutions:

• Questions similar to this exercise:

C2 Exercise 1C

• C2 Exercise 1C worked solutions:

• Questions similar to this exercise:

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C2 section 1.3

You need to already know how to do sections 1.1 and 1.2 above and how to reliably substitute values into functions to evaluate f (k) for any polynomial function P = f (x) at some particular value of x = k

You will learn how to use the factor theorem which states that when f(k) = 0 we can be sure that (x - k) is a factor of the polynomial P = f (x) and vice versa that when (x - k)is a factor, we get f(k) = 0. This is why American texts call roots of equations 'zeros.'

Examples:

C2 Exercise 1D

• C2 Exercise 1D worked solutions:

• Questions similar to this exercise:

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C2 section 1.4

You need to already know how to do sections 1.1 through 1.3 above and how to reliably substitute values into functions to evaluate f (a/b) for any polynomial function P = f (x) at some particular fractional value of x = a/b

You will learn how to use and interpret the remainder theorem which states that when f(a/b) = k we can be sure that (bx - a) leaves remainder k when the polynomial P = f (x) is divided by the binomial (bx - a).

Examples:

C2 Exercise 1E

• C2 Exercise 1E worked solutions:

• Questions similar to this exercise:

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C2 chapter 1 miscellany

C2 Exercise 1F

• C2 Exercise 1F worked solutions:

• Questions similar to this exercise: